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Modeling Interfacial Tension of Heptane + Alcohol Mixtures Using Cubic Plus Association Equation of State Plus Simplified Gradient Theory

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Abstract

This work has been dedicated to modeling the interfacial tension of the heptane + alcohol mixtures in the temperature range of 288.15 K to 333.15 K. The cubic plus association equation of state is applied to the liquid–vapor phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental isothermal and isobaric phase equilibrium data. For the binary interaction parameters, correlations have been obtained as a function of temperature for isothermal phase equilibrium, and a constant value for isobaric phase equilibrium. The linear gradient theory is used as a predictive and adjustment approach to describe the interfacial tension of the heptane + alcohol mixtures. The influence parameters of the pure components were constant and the symmetric parameters of the binary mixtures were correlated with the temperature. The results of this work show that the cubic plus association equation of state is capable of simultaneously representing the phase equilibrium and interfacial tension of the mixtures studied. The results obtained in the interfacial tension are in agreement with those published in the literature.

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Abbreviations

a :

Attractive parameter in CPA-EOS

\(a_0\) :

Adjustable parameter of the CPA-EOS

AAD:

statistical deviation

b :

Covolume parameter in the CPA-EOS

C :

Number of carbons in the alcohol

c :

Influence parameter

c 1 :

Adjustable parameter of the CPA EOS

f 0 :

Helmholtz energy density

g :

The radial distribution function

\(k_{ij}\) :

Interaction parameter in the CPA-EOS

n :

Number of points

\(n_c\) :

Number of components

P :

Absolute pressure

R :

Universal gas constant

T :

Absolute temperature

x :

Mole fraction of the liquid phase

\(X_{A_i}\) :

The mole fraction of the molecule i not bonded at site A

z :

Position in the interface

\(\beta ^{A_i B_i}\) :

The association volume

\(\beta _{ij}\) :

Symmetric parameter

\(\Delta ^{A_i B_j}\) :

The association strength

\(\epsilon ^{A_i B_i}\) :

The association energy

\(\eta\) :

Reduced density

\(\mu\) :

Chemical potential

\(\Omega\) :

Grand thermodynamic potential

\(\rho\) :

Molar concentration

\(\sigma\) :

Interfacial tension

c :

Critical condition

i, j, s :

Species

0:

Equilibrium condition

exp :

Experimental

L :

Liquid phase

theo :

Theoretical

V :

Vapor phase

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Acknowledgments

A.H acknowledges the economic support given by the UCSC.

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  1. Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile

    Ariel Hernández

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Hernández, A. Modeling Interfacial Tension of Heptane + Alcohol Mixtures Using Cubic Plus Association Equation of State Plus Simplified Gradient Theory. Int J Thermophys 44, 16 (2023). https://doi.org/10.1007/s10765-022-03126-6

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